Exam P topic · 23–30% syllabus weight

Exam P General Probability practice problems

Independently written solutions mapped to this official syllabus topic. Pages appear only after all required checks agree.

Topic orientation

What this topic tests

General Probability connects event algebra, conditional probability, independence, counting, and Bayes’ theorem. The main work is usually translating a verbal experiment into events whose intersections and complements can be calculated cleanly.

Exam questions often hide the decisive denominator or conditioning event inside the setup. A strong solution names the event first, checks that the pieces form a valid probability model, and only then substitutes numbers.

Typical failure modes

  • Using an unconditional probability where a conditional denominator is required
  • Treating mutually exclusive events as independent
  • Forgetting a complement or double-counting overlapping cases

Published ledger

Exam P General Probability practice problems and solutions

Each entry shows its independent calculation record and links to the official source without reproducing protected wording.

  1. SOA Exam P Sample Question #1General Probability · Inclusion–ExclusionVerified
  2. SOA Exam P Sample Question #2General Probability · Inclusion–ExclusionVerified
  3. SOA Exam P Sample Question #3General Probability · Inclusion–ExclusionVerified
  4. SOA Exam P Sample Question #4General Probability · IndependenceVerified
  5. SOA Exam P Sample Question #5General Probability · Inclusion–ExclusionVerified
  6. SOA Exam P Sample Question #6General Probability · Conditional ProbabilityVerified
  7. SOA Exam P Sample Question #7General Probability · Expected ValueVerified
  8. SOA Exam P Sample Question #8General Probability · Inclusion–ExclusionVerified
  9. SOA Exam P Sample Question #9General Probability · Conditional ProbabilityVerified
  10. SOA Exam P Sample Question #10General Probability · IndependenceVerified
  11. SOA Exam P Sample Question #11General Probability · Inclusion–ExclusionVerified
  12. SOA Exam P Sample Question #12General Probability · Conditional Probability · Inclusion–ExclusionVerified
  13. SOA Exam P Sample Question #14General Probability · Expected ValueVerified
  14. SOA Exam P Sample Question #16General Probability · IndependenceVerified
  15. SOA Exam P Sample Question #18General Probability · Bayes’ TheoremVerified
  16. SOA Exam P Sample Question #19General Probability · Bayes’ TheoremVerified
  17. SOA Exam P Sample Question #20General Probability · Bayes’ TheoremVerified
  18. SOA Exam P Sample Question #21General Probability · Bayes’ TheoremVerified
  19. SOA Exam P Sample Question #22General Probability · Bayes’ TheoremVerified
  20. SOA Exam P Sample Question #24General Probability · Bayes’ TheoremVerified
  21. SOA Exam P Sample Question #25General Probability · Bayes’ TheoremVerified
  22. SOA Exam P Sample Question #26General Probability · Bayes’ TheoremVerified
  23. SOA Exam P Sample Question #27General Probability · Bayes’ Theorem · Binomial DistributionVerified
  24. SOA Exam P Sample Question #74General Probability · Binomial Distribution · Expected Value · Indicator VariablesVerified
  25. SOA Exam P Sample Question #81General Probability · Conditional Probability · Expected Value · Life ContingenciesVerified
  26. SOA Exam P Sample Question #84General Probability · Law of Total Probability · Mixture Distributions · Exponential DistributionVerified
  27. SOA Exam P Sample Question #85General Probability · Discrete Distributions · Arithmetic Probability SequencesVerified
  28. SOA Exam P Sample Question #87General Probability · Set Probability · Inclusion–ExclusionVerified
  29. SOA Exam P Sample Question #90General Probability · Hypergeometric Distribution · Sampling Without ReplacementVerified
  30. SOA Exam P Sample Question #92General Probability · Probability Modeling · RatiosVerified
  31. SOA Exam P Sample Question #94General Probability · Conditional Expectation · Geometric Distribution · Memoryless PropertyVerified
  32. SOA Exam P Sample Question #97General Probability · Combinatorics · CountingVerified
  33. SOA Exam P Sample Question #98General Probability · Expected Value · Mixture Distributions · Indicator VariablesVerified
  34. SOA Exam P Sample Question #99General Probability · Set Probability · Inclusion–Exclusion · ComplementsVerified
  35. SOA Exam P Sample Question #100General Probability · Inclusion-ExclusionVerified
  36. SOA Exam P Sample Question #105General Probability · Hypergeometric SamplingVerified
  37. SOA Exam P Sample Question #108General Probability · Geometric-Series ProbabilityVerified
  38. SOA Exam P Sample Question #113General Probability · Equally Likely Outcome CountingVerified
  39. SOA Exam P Sample Question #120General Probability · Event IndependenceVerified
  40. SOA Exam P Sample Question #121General Probability · Mixture ProbabilityVerified
  41. SOA Exam P Sample Question #122General Probability · Conditional Hypergeometric CountingVerified
  42. SOA Exam P Sample Question #127General Probability · Bayes RuleVerified
  43. SOA Exam P Sample Question #128General Probability · Hypergeometric SamplingVerified
  44. SOA Exam P Sample Question #130General Probability · Inclusion-Exclusion · Complements · Joint ProbabilityVerified
  45. SOA Exam P Sample Question #132General Probability · Conditional Probability · Contingency Tables · Total ProbabilityVerified
  46. SOA Exam P Sample Question #133General Probability · Bayes' Theorem · Conditional Probability · Total ProbabilityVerified
  47. SOA Exam P Sample Question #134General Probability · Discrete Sample Spaces · Combinatorial Probability · Lattice CountingVerified
  48. SOA Exam P Sample Question #135General Probability · Conditional ProbabilityVerified
  49. SOA Exam P Sample Question #138General Probability · Conditional Outcome CountingVerified
  50. SOA Exam P Sample Question #147General Probability · Mutually Exclusive Outcomes · Complements · Systems of ProbabilitiesVerified
  51. SOA Exam P Sample Question #150General Probability · Conditional Probability · Bayes’ Theorem · Discrete Uniform DistributionVerified
  52. SOA Exam P Sample Question #151General Probability · Conditional Probability · Bayes’ Theorem · Law of Total ProbabilityVerified
  53. SOA Exam P Sample Question #153General Probability · Events and Set Operations · Intersections · Logical EquivalenceVerified
  54. SOA Exam P Sample Question #154General Probability · Law of Total Probability · Mixture Distributions · Conditional ProbabilityVerified
  55. SOA Exam P Sample Question #156General Probability · Hypergeometric Distribution · Sampling Without Replacement · Combinatorial ProbabilityVerified
  56. SOA Exam P Sample Question #157General Probability · Sampling Without Replacement · Combinatorial Probability · Hypergeometric DistributionVerified
  57. SOA Exam P Sample Question #182General Probability · Set Operations · Venn Diagrams · CountingVerified
  58. SOA Exam P Sample Question #183General Probability · Set Operations · Venn Diagrams · CountingVerified
  59. SOA Exam P Sample Question #184General Probability · Inclusion-Exclusion · Set Complements · Venn DiagramsVerified
  60. SOA Exam P Sample Question #185General Probability · Counting Techniques · Combinations · PermutationsVerified
  61. SOA Exam P Sample Question #186General Probability · Conditional Probability · Hypergeometric Distribution · Sampling Without ReplacementVerified
  62. SOA Exam P Sample Question #187General Probability · Mixture Distributions · Binomial Distribution · IndependenceVerified
  63. SOA Exam P Sample Question #188General Probability · Independence · Mutually Exclusive Events · Event AlgebraVerified
  64. SOA Exam P Sample Question #191General Probability · Inclusion–Exclusion · Independence · Mutually Exclusive EventsVerified
  65. SOA Exam P Sample Question #192General Probability · Mutually Exclusive Events · Event Algebra · Union ProbabilityVerified
  66. SOA Exam P Sample Question #193General Probability · Permutations · Inclusion–Exclusion · DerangementsVerified
  67. SOA Exam P Sample Question #194General Probability · Conditional Probability · Discrete Random Variables · DeductiblesVerified
  68. SOA Exam P Sample Question #195General Probability · Conditional Probability · Inclusion–Exclusion · Joint ProbabilityVerified
  69. SOA Exam P Sample Question #196General Probability · Hypergeometric Distribution · Sampling Without Replacement · CombinationsVerified
  70. SOA Exam P Sample Question #197General Probability · Sampling Without Replacement · Sequential Probability · Pigeonhole PrincipleVerified
  71. SOA Exam P Sample Question #198General Probability · Conditional Probability · Bayes' Theorem · Law of Total ProbabilityVerified
  72. SOA Exam P Sample Question #199General Probability · Conditional Probability · Bayes' Theorem · Law of Total ProbabilityVerified
  73. SOA Exam P Sample Question #210General Probability · Independence · Complements · Event AlgebraVerified
  74. SOA Exam P Sample Question #211General Probability · Geometric Distribution · Conditional Probability · IndependenceVerified
  75. SOA Exam P Sample Question #233General Probability · Hypergeometric Distribution · Conditional Distributions · VarianceVerified
  76. SOA Exam P Sample Question #237General Probability · Continuous Uniform Distribution · Independence · Inclusion–ExclusionVerified
  77. SOA Exam P Sample Question #258General Probability · Set Counting · Inclusion-Exclusion · Venn DiagramsVerified
  78. SOA Exam P Sample Question #259General Probability · Conditional Probability · Set Operations · ComplementsVerified
  79. SOA Exam P Sample Question #263General Probability · Independence · Conditional Probability · Complement RuleVerified
  80. SOA Exam P Sample Question #264General Probability · Bayes' Theorem · Conditional Probability · Law of Total ProbabilityVerified
  81. SOA Exam P Sample Question #265General Probability · Law of Total Probability · Bayes' Theorem · Conditional ProbabilityVerified
  82. SOA Exam P Sample Question #274General Probability · Conditional Probability · Inclusion-Exclusion · Set ProbabilityVerified
  83. SOA Exam P Sample Question #288General Probability · Conditional Probability · Bayes' Theorem · Diagnostic TestingVerified
  84. SOA Exam P Sample Question #295General Probability · Independence · Bernoulli Random Variables · Poisson Binomial DistributionVerified
  85. SOA Exam P Sample Question #296General Probability · Contingency Tables · Systems of EquationsVerified
  86. SOA Exam P Sample Question #304General Probability · Sampling Without Replacement · Hypergeometric Distribution · Complement RuleVerified
  87. SOA Exam P Sample Question #306General Probability · Bayes' Theorem · Exponential Distribution · Survival ProbabilitiesVerified
  88. SOA Exam P Sample Question #309General Probability · Bayes' Theorem · Law of Total Probability · Conditional ProbabilityVerified
  89. SOA Exam P Sample Question #312General Probability · Conditional Probability · Set Operations · Inclusion-ExclusionVerified
  90. SOA Exam P Sample Question #313General Probability · Independence · Joint ProbabilitiesVerified
  91. SOA Exam P Sample Question #314General Probability · Bayes' Theorem · Poisson Distribution · Mixture DistributionsVerified
  92. SOA Exam P Sample Question #316General Probability · Bayes' Theorem · Law of Total Probability · Conditional ProbabilityVerified
  93. SOA Exam P Sample Question #318General Probability · Bayes' Theorem · Law of Total Probability · Conditional ProbabilityVerified
  94. SOA Exam P Sample Question #319General Probability · Independence · Bernoulli Random Variables · Poisson Binomial DistributionVerified
  95. SOA Exam P Sample Question #323General Probability · Independence · Bernoulli Random Variables · Poisson Binomial DistributionVerified
  96. SOA Exam P Sample Question #325General Probability · Set Probability · Indicator Random Variables · Systems of EquationsVerified
  97. SOA Exam P Sample Question #329General Probability · Bayes' Theorem · Conditional Probability · Law of Total ProbabilityVerified
  98. SOA Exam P Sample Question #331General Probability · Set Operations · Venn Diagrams · Exclusive Event RegionsVerified
  99. SOA Exam P Sample Question #332General Probability · Counting Principles · Equally Likely Outcomes · Occupancy PatternsVerified
  100. SOA Exam P Sample Question #333General Probability · Hypergeometric Distribution · Sampling Without Replacement · Combinatorial ProbabilityVerified
  101. SOA Exam P Sample Question #334General Probability · Bayes' Theorem · Conditional ProbabilityVerified
  102. SOA Exam P Sample Question #335General Probability · Hypergeometric Distribution · Sampling Without Replacement · Combinatorial ProbabilityVerified
  103. SOA Exam P Sample Question #346General Probability · Inclusion–Exclusion · Set Probability · Mutually Exclusive EventsVerified
  104. SOA Exam P Sample Question #348General Probability · Independence · Complements · Uniform DistributionVerified
  105. SOA Exam P Sample Question #349General Probability · Law of Total Probability · Conditional Probability · Joint ProbabilityVerified
  106. SOA Exam P Sample Question #351General Probability · Independence · Bernoulli Random Variables · Poisson Binomial DistributionVerified
  107. SOA Exam P Sample Question #354General Probability · Conditional Probability · ComplementsVerified
  108. SOA Exam P Sample Question #359General Probability · Bayes' Theorem · Law of Total ProbabilityVerified
  109. SOA Exam P Sample Question #360Univariate Random Variables · Discrete Random Variables · Expected Value · General ProbabilityVerified
  110. SOA Exam P Sample Question #363General Probability · Law of Total Probability · Bayes' Theorem · Conditional ProbabilityVerified
  111. SOA Exam P Sample Question #365General Probability · Conditional Probability · Complements · Set ProbabilityVerified
  112. SOA Exam P Sample Question #366General Probability · Hypergeometric Distribution · Sampling Without Replacement · Combinatorial ProbabilityVerified
  113. SOA Exam P Sample Question #367General Probability · Inclusion–Exclusion · Set Probability · Counting MethodsVerified
  114. SOA Exam P Sample Question #368General Probability · Inclusion–Exclusion · Conditional Probability · Set ProbabilityVerified
  115. SOA Exam P Sample Question #369General Probability · Independence · Complements · Survival ProbabilitiesVerified
  116. SOA Exam P Sample Question #370General Probability · Law of Total Probability · Bayes' Theorem · Conditional ProbabilityVerified
  117. SOA Exam P Sample Question #376General Probability · Hypergeometric Distribution · Sampling Without ReplacementVerified
  118. SOA Exam P Sample Question #377General Probability · Conditional Probability · Contingency TablesVerified
  119. SOA Exam P Sample Question #387General Probability · Conditional Probability · Combinatorial Probability · Sampling Without ReplacementVerified
  120. SOA Exam P Sample Question #389General Probability · Counting Methods · Permutations and Placement · Combinatorial ProbabilityVerified
  121. SOA Exam P Sample Question #398General Probability · Bayes Theorem · Conditional Probability · Predictive ProbabilityVerified
  122. SOA Exam P Sample Question #399General Probability · Multinomial Distribution · Negative Binomial DistributionVerified
  123. SOA Exam P Sample Question #403General Probability · Counting Methods · Sampling Without ReplacementVerified
  124. SOA Exam P Sample Question #405General Probability · Expected Value · Counting Methods · Linearity of ExpectationVerified
  125. SOA Exam P Sample Question #408General Probability · Conditional Probability · Bayes' Theorem · Predictive ProbabilityVerified
  126. SOA Exam P Sample Question #414General Probability · Combinatorial Probability · Hypergeometric Distribution · Sampling Without ReplacementVerified
  127. SOA Exam P Sample Question #415General Probability · Inclusion-Exclusion · Expected Value · Joint ProbabilitiesVerified
  128. SOA Exam P Sample Question #418General Probability · Conditional Probability · Independence · Discrete Random VariablesVerified
  129. SOA Exam P Sample Question #422General Probability · Mutually Exclusive Events · Set Probability · Law of Total ProbabilityVerified
  130. SOA Exam P Sample Question #423General Probability · Conditional Probability · Contingency TablesVerified
  131. SOA Exam P Sample Question #424General Probability · Counting Methods · Permutations and PlacementVerified
  132. SOA Exam P Sample Question #437General Probability · Discrete Random Variables · Probability ReconstructionVerified
  133. SOA Exam P Sample Question #438General Probability · Hypergeometric Distribution · Sampling Without ReplacementVerified
  134. SOA Exam P Sample Question #445General Probability · Set Probability · Inclusion-Exclusion · Venn DiagramsVerified
  135. SOA Exam P Sample Question #455General Probability · Conditional Probability · Bayes' Theorem · Poisson DistributionVerified
  136. SOA Exam P Sample Question #456General Probability · Hypergeometric Distribution · Sampling Without ReplacementVerified
  137. SOA Exam P Sample Question #460General Probability · Conditional Probability · Mixture DistributionsVerified
  138. SOA Exam P Sample Question #468General Probability · Conditional Probability · Law of Total Probability · Latent MixturesVerified
  139. SOA Exam P Sample Question #472General Probability · Binomial Distribution · Independent Trials · Probability RatiosVerified
  140. SOA Exam P Sample Question #486General Probability · Independence · Complement Rule · Binomial DistributionVerified
  141. SOA Exam P Sample Question #487General Probability · Conditional Probability · Nested Events · Set ProbabilityVerified
  142. SOA Exam P Sample Question #490General Probability · Conditional Probability · Independent Bernoulli TrialsVerified
  143. SOA Exam P Sample Question #493General Probability · Conditional Probability · Joint Distributions · Probability TablesVerified
  144. SOA Exam P Sample Question #498General Probability · Conditional Probability · Bayes' TheoremVerified
  145. SOA Exam P Sample Question #500General Probability · Independence · Binomial Distribution · Algebraic IdentitiesVerified
  146. SOA Exam P Sample Question #501General Probability · Conditional Probability · Combinatorial Probability · Hypergeometric DistributionVerified
  147. SOA Exam P Sample Question #506General Probability · Conditional Probability · Bayes' TheoremVerified
  148. SOA Exam P Sample Question #524General Probability · Combinatorial Probability · Category-Constrained SelectionsVerified
  149. SOA Exam P Sample Question #528General Probability · Conditional Probability · Set ProbabilityVerified
  150. SOA Exam P Sample Question #530General Probability · Law of Total Probability · Discrete Sample SpacesVerified
  151. SOA Exam P Sample Question #531General Probability · Independence · Mutually Exclusive Events · ComplementsVerified
  152. SOA Exam P Sample Question #532General Probability · Conditional Probability · Bayes' TheoremVerified
  153. SOA Exam P Sample Question #533General Probability · Conditional Probability · Combinatorial Probability · ExchangeabilityVerified
  154. SOA Exam P Sample Question #536General Probability · Set Probability · Disjoint EventsVerified
  155. SOA Exam P Sample Question #537General Probability · Conditional Probability · Complement RuleVerified
  156. SOA Exam P Sample Question #540General Probability · Bayes Theorem · Conditional ProbabilityVerified
  157. SOA Exam P Sample Question #544General Probability · Conditional Probability · Compound DistributionsVerified
  158. SOA Exam P Sample Question #546General Probability · Bayes' Theorem · Diagnostic TestingVerified
  159. SOA Exam P Sample Question #547General Probability · Bayes' Theorem · Binary ChannelsVerified
  160. SOA Exam P Sample Question #548General Probability · Sampling Without Replacement · Law of Total ProbabilityVerified
  161. SOA Exam P Sample Question #549General Probability · Combinatorial Probability · Circular ArrangementsVerified
  162. SOA Exam P Sample Question #550General Probability · Combinatorial Probability · Category-Constrained SelectionsVerified
  163. SOA Exam P Sample Question #561General Probability · Combinatorial Probability · Sampling Without ReplacementVerified
  164. SOA Exam P Sample Question #570General Probability · Counting Methods · Sampling Without ReplacementVerified
  165. SOA Exam P Sample Question #572General Probability · Bayes' Theorem · Poisson DistributionVerified
  166. SOA Exam P Sample Question #590General Probability · Geometric Distribution · IndependenceVerified
  167. SOA Exam P Sample Question #594General Probability · Sampling Without Replacement · Hypergeometric DistributionVerified
  168. SOA Exam P Sample Question #602General Probability · Discrete Random Variables · Cumulative Probabilities · Probability RatiosVerified
  169. SOA Exam P Sample Question #603General Probability · Bayes' Theorem · Poisson Distribution · Mixture DistributionsVerified
  170. SOA Exam P Sample Question #605General Probability · Bayes' Theorem · Exponential Distribution · Mixture DistributionsVerified
  171. SOA Exam P Sample Question #607General Probability · Disjoint Events · Interval ProbabilitiesVerified
  172. SOA Exam P Sample Question #620General Probability · Independence · Sums of Independent Random VariablesVerified
  173. SOA Exam P Sample Question #640General Probability · Conditional Probability · Binomial DistributionVerified
  174. SOA Exam P Sample Question #641General Probability · Conditional Probability · IndependenceVerified
  175. SOA Exam P Sample Question #644General Probability · Conditional Probability · Combinatorial Probability · ExchangeabilityVerified
  176. SOA Exam P Sample Question #645General Probability · Conditional Probability · Independence · Combinatorial ProbabilityVerified
  177. SOA Exam P Sample Question #646General Probability · Complement Rule · IndependenceVerified
  178. SOA Exam P Sample Question #647General Probability · Law of Total Probability · Mixture DistributionsVerified
  179. SOA Exam P Sample Question #653General Probability · Independence · Complement RuleVerified
  180. SOA Exam P Sample Question #657General Probability · Inclusion–Exclusion · Probability BoundsVerified
  181. SOA Exam P Sample Question #658General Probability · Conditional Probability · Inclusion–ExclusionVerified
  182. SOA Exam P Sample Question #663General Probability · Conditional Probability · Normal Distribution · StandardizationVerified
  183. SOA Exam P Sample Question #682General Probability · Conditional Probability · Binomial DistributionVerified
  184. SOA Exam P Sample Question #683General Probability · Conditional Probability · Inclusion–ExclusionVerified
  185. SOA Exam P Sample Question #685General Probability · Conditional Probability · IndependenceVerified
  186. SOA Exam P Sample Question #688General Probability · Counting Methods · Sampling Without ReplacementVerified
  187. SOA Exam P Sample Question #691General Probability · Set Probability · Complements · Mutually Exclusive EventsVerified
  188. SOA Exam P Sample Question #694General Probability · Hypergeometric Distribution · Sampling Without ReplacementVerified
  189. SOA Exam P Sample Question #699General Probability · Bayes' Theorem · Poisson DistributionVerified
  190. SOA Exam P Sample Question #701General Probability · Discrete Random Variables · Geometric SeriesVerified
  191. SOA Exam P Sample Question #723General Probability · Law of Total Probability · Mixture ProbabilitiesVerified
  192. SOA Exam P Sample Question #733General Probability · Conditional Probability · Set ProbabilityVerified

Drill one method at a time

Techniques that keep appearing in General Probability

Each guide collects the questions above that turn on the same method, with the formulas and the errors that cost marks.

57 worked solutions

Exam P Variance problems

Second moments, transformations, sums, covariance terms, and conditional variance decompositions.

55 worked solutions

Exam P Independence problems

Event independence, factorization, independent trials, and the consequences independence does—and does not—justify.

46 worked solutions

Exam P Expected Value problems

Discrete sums, continuous integrals, functions of loss, linearity, conditioning, and tail-based expectation.

Study the whole topic offline

Every Exam P sample question in one searchable PDF

The 192 pages above stay free. The manual collects the complete Exam P sample set in syllabus order, with the same working, the wrong-choice notes, and one new practice problem per question.